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<div class="title">arch/MSA/MathFunctions.h</div>  </div>
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<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2007 Julien Pommier</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">// Copyright (C) 2014 Pedro Gonnet (pedro.gonnet@gmail.com)</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// Copyright (C) 2016 Gael Guennebaud &lt;gael.guennebaud@inria.fr&gt;</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// Copyright (C) 2018 Wave Computing, Inc.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">// Written by:</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment">//   Chris Larsen</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="comment">//   Alexey Frunze (afrunze@wavecomp.com)</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160; </div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="comment">/* The sin, cos, exp, and log functions of this file come from</span></div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="comment"> * Julien Pommier&#39;s sse math library: http://gruntthepeon.free.fr/ssemath/</span></div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160; </div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="comment">/* The tanh function of this file is an adaptation of</span></div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="comment"> * template&lt;typename T&gt; T generic_fast_tanh_float(const T&amp;)</span></div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="comment"> * from MathFunctionsImpl.h.</span></div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160; </div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="preprocessor">#ifndef EIGEN_MATH_FUNCTIONS_MSA_H</span></div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;<span class="preprocessor">#define EIGEN_MATH_FUNCTIONS_MSA_H</span></div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160; </div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;<span class="preprocessor">#include &quot;../../InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160; </div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160; </div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160; </div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;plog&lt;Packet4f&gt;(<span class="keyword">const</span> Packet4f&amp; _x) {</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292e-2f);</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, -1.1514610310e-1f);</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740e-1f);</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, -1.2420140846e-1f);</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, +1.4249322787e-1f);</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, -1.6668057665e-1f);</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, +2.0000714765e-1f);</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, -2.4999993993e-1f);</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, +3.3333331174e-1f);</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(1, 1.0f);</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160; </div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;  <span class="comment">// Convert negative argument into NAN (quiet negative, to be specific).</span></div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;  Packet4f zero = (Packet4f)__builtin_msa_ldi_w(0);</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;  Packet4i neg_mask = __builtin_msa_fclt_w(_x, zero);</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;  Packet4i zero_mask = __builtin_msa_fceq_w(_x, zero);</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;  Packet4f non_neg_x_or_nan = padd(_x, (Packet4f)neg_mask);  <span class="comment">// Add 0.0 or NAN.</span></div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;  Packet4f x = non_neg_x_or_nan;</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160; </div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;  <span class="comment">// Extract exponent from x = mantissa * 2**exponent, where 1.0 &lt;= mantissa &lt; 2.0.</span></div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;  <span class="comment">// N.B. the exponent is one less of what frexpf() would return.</span></div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;  Packet4i e_int = __builtin_msa_ftint_s_w(__builtin_msa_flog2_w(x));</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;  <span class="comment">// Multiply x by 2**(-exponent-1) to get 0.5 &lt;= x &lt; 1.0 as from frexpf().</span></div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;  x = __builtin_msa_fexp2_w(x, (Packet4i)__builtin_msa_nori_b((v16u8)e_int, 0));</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160; </div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;  <span class="comment">/*</span></div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;<span class="comment">     if (x &lt; SQRTHF) {</span></div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;<span class="comment">       x = x + x - 1.0;</span></div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;<span class="comment">     } else {</span></div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;<span class="comment">       e += 1;</span></div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;<span class="comment">       x = x - 1.0;</span></div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;<span class="comment">     }</span></div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;<span class="comment">  */</span></div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;  Packet4f xx = padd(x, x);</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;  Packet4i ge_mask = __builtin_msa_fcle_w(p4f_cephes_SQRTHF, x);</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;  e_int = psub(e_int, ge_mask);</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;  x = (Packet4f)__builtin_msa_bsel_v((v16u8)ge_mask, (v16u8)xx, (v16u8)x);</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;  x = psub(x, p4f_1);</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;  Packet4f e = __builtin_msa_ffint_s_w(e_int);</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160; </div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;  Packet4f x2 = pmul(x, x);</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;  Packet4f x3 = pmul(x2, x);</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160; </div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;  Packet4f y, y1, y2;</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;  y = pmadd(p4f_cephes_log_p0, x, p4f_cephes_log_p1);</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;  y1 = pmadd(p4f_cephes_log_p3, x, p4f_cephes_log_p4);</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;  y2 = pmadd(p4f_cephes_log_p6, x, p4f_cephes_log_p7);</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;  y = pmadd(y, x, p4f_cephes_log_p2);</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;  y1 = pmadd(y1, x, p4f_cephes_log_p5);</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;  y2 = pmadd(y2, x, p4f_cephes_log_p8);</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;  y = pmadd(y, x3, y1);</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;  y = pmadd(y, x3, y2);</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;  y = pmul(y, x3);</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160; </div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;  y = pmadd(e, p4f_cephes_log_q1, y);</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;  x = __builtin_msa_fmsub_w(x, x2, p4f_half);</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;  x = padd(x, y);</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;  x = pmadd(e, p4f_cephes_log_q2, x);</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160; </div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;  <span class="comment">// x is now the logarithm result candidate. We still need to handle the</span></div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;  <span class="comment">// extreme arguments of zero and positive infinity, though.</span></div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;  <span class="comment">// N.B. if the argument is +INFINITY, x is NAN because the polynomial terms</span></div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;  <span class="comment">// contain infinities of both signs (see the coefficients and code above).</span></div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;  <span class="comment">// INFINITY - INFINITY is NAN.</span></div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160; </div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;  <span class="comment">// If the argument is +INFINITY, make it the new result candidate.</span></div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;  <span class="comment">// To achieve that we choose the smaller of the result candidate and the</span></div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;  <span class="comment">// argument.</span></div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;  <span class="comment">// This is correct for all finite pairs of values (the logarithm is smaller</span></div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;  <span class="comment">// than the argument).</span></div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;  <span class="comment">// This is also correct in the special case when the argument is +INFINITY</span></div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;  <span class="comment">// and the result candidate is NAN. This is because the fmin.df instruction</span></div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;  <span class="comment">// prefers non-NANs to NANs.</span></div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;  x = __builtin_msa_fmin_w(x, non_neg_x_or_nan);</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160; </div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;  <span class="comment">// If the argument is zero (including -0.0), the result becomes -INFINITY.</span></div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;  Packet4i neg_infs = __builtin_msa_slli_w(zero_mask, 23);</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;  x = (Packet4f)__builtin_msa_bsel_v((v16u8)zero_mask, (v16u8)x, (v16u8)neg_infs);</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160; </div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;  <span class="keywordflow">return</span> x;</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;}</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160; </div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;pexp&lt;Packet4f&gt;(<span class="keyword">const</span> Packet4f&amp; _x) {</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;  <span class="comment">// Limiting single-precision pexp&#39;s argument to [-128, +128] lets pexp</span></div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;  <span class="comment">// reach 0 and INFINITY naturally.</span></div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(exp_lo, -128.0f);</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(exp_hi, +128.0f);</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500e-4f);</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507e-3f);</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073e-3f);</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894e-2f);</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459e-1f);</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201e-1f);</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(1, 1.0f);</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160; </div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;  Packet4f x = _x;</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160; </div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;  <span class="comment">// Clamp x.</span></div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;  x = (Packet4f)__builtin_msa_bsel_v((v16u8)__builtin_msa_fclt_w(x, p4f_exp_lo), (v16u8)x,</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;                                     (v16u8)p4f_exp_lo);</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;  x = (Packet4f)__builtin_msa_bsel_v((v16u8)__builtin_msa_fclt_w(p4f_exp_hi, x), (v16u8)x,</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;                                     (v16u8)p4f_exp_hi);</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160; </div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;  <span class="comment">// Round to nearest integer by adding 0.5 (with x&#39;s sign) and truncating.</span></div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;  Packet4f x2_add = (Packet4f)__builtin_msa_binsli_w((v4u32)p4f_half, (v4u32)x, 0);</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;  Packet4f x2 = pmadd(x, p4f_cephes_LOG2EF, x2_add);</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;  Packet4i x2_int = __builtin_msa_ftrunc_s_w(x2);</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;  Packet4f x2_int_f = __builtin_msa_ffint_s_w(x2_int);</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160; </div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;  x = __builtin_msa_fmsub_w(x, x2_int_f, p4f_cephes_exp_C1);</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;  x = __builtin_msa_fmsub_w(x, x2_int_f, p4f_cephes_exp_C2);</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160; </div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;  Packet4f z = pmul(x, x);</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160; </div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;  Packet4f y = p4f_cephes_exp_p0;</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;  y = pmadd(y, x, p4f_cephes_exp_p1);</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;  y = pmadd(y, x, p4f_cephes_exp_p2);</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;  y = pmadd(y, x, p4f_cephes_exp_p3);</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;  y = pmadd(y, x, p4f_cephes_exp_p4);</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;  y = pmadd(y, x, p4f_cephes_exp_p5);</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;  y = pmadd(y, z, x);</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;  y = padd(y, p4f_1);</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160; </div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;  <span class="comment">// y *= 2**exponent.</span></div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;  y = __builtin_msa_fexp2_w(y, x2_int);</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160; </div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;  <span class="keywordflow">return</span> y;</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;}</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160; </div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;ptanh&lt;Packet4f&gt;(<span class="keyword">const</span> Packet4f&amp; _x) {</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(tanh_tiny, 1e-4f);</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(tanh_hi, 9.0f);</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;  <span class="comment">// The monomial coefficients of the numerator polynomial (odd).</span></div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(alpha_1, 4.89352455891786e-3f);</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(alpha_3, 6.37261928875436e-4f);</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(alpha_5, 1.48572235717979e-5f);</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(alpha_7, 5.12229709037114e-8f);</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(alpha_9, -8.60467152213735e-11f);</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(alpha_11, 2.00018790482477e-13f);</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(alpha_13, -2.76076847742355e-16f);</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;  <span class="comment">// The monomial coefficients of the denominator polynomial (even).</span></div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(beta_0, 4.89352518554385e-3f);</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(beta_2, 2.26843463243900e-3f);</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(beta_4, 1.18534705686654e-4f);</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(beta_6, 1.19825839466702e-6f);</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160; </div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;  Packet4f x = pabs(_x);</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;  Packet4i tiny_mask = __builtin_msa_fclt_w(x, p4f_tanh_tiny);</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160; </div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;  <span class="comment">// Clamp the inputs to the range [-9, 9] since anything outside</span></div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;  <span class="comment">// this range is -/+1.0f in single-precision.</span></div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;  x = (Packet4f)__builtin_msa_bsel_v((v16u8)__builtin_msa_fclt_w(p4f_tanh_hi, x), (v16u8)x,</div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;                                     (v16u8)p4f_tanh_hi);</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160; </div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;  <span class="comment">// Since the polynomials are odd/even, we need x**2.</span></div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;  Packet4f x2 = pmul(x, x);</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160; </div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;  <span class="comment">// Evaluate the numerator polynomial p.</span></div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;  Packet4f p = pmadd(x2, p4f_alpha_13, p4f_alpha_11);</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;  p = pmadd(x2, p, p4f_alpha_9);</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;  p = pmadd(x2, p, p4f_alpha_7);</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;  p = pmadd(x2, p, p4f_alpha_5);</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;  p = pmadd(x2, p, p4f_alpha_3);</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;  p = pmadd(x2, p, p4f_alpha_1);</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;  p = pmul(x, p);</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160; </div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;  <span class="comment">// Evaluate the denominator polynomial q.</span></div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;  Packet4f q = pmadd(x2, p4f_beta_6, p4f_beta_4);</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;  q = pmadd(x2, q, p4f_beta_2);</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;  q = pmadd(x2, q, p4f_beta_0);</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160; </div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;  <span class="comment">// Divide the numerator by the denominator.</span></div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;  p = pdiv(p, q);</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160; </div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;  <span class="comment">// Reinstate the sign.</span></div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;  p = (Packet4f)__builtin_msa_binsli_w((v4u32)p, (v4u32)_x, 0);</div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160; </div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;  <span class="comment">// When the argument is very small in magnitude it&#39;s more accurate to just return it.</span></div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;  p = (Packet4f)__builtin_msa_bsel_v((v16u8)tiny_mask, (v16u8)p, (v16u8)_x);</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160; </div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;  <span class="keywordflow">return</span> p;</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;}</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160; </div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">bool</span> sine&gt;</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;Packet4f psincos_inner_msa_float(<span class="keyword">const</span> Packet4f&amp; _x) {</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(sincos_max_arg, 13176795.0f);  <span class="comment">// Approx. (2**24) / (4/Pi).</span></div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1, -0.78515625f);</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891e-4f);</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736e-3f);</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611e-1f);</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948e-5f);</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765e-3f);</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827e-2f);</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f);  <span class="comment">// 4/Pi.</span></div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);</div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(1, 1.0f);</div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160; </div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;  Packet4f x = pabs(_x);</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160; </div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;  <span class="comment">// Translate infinite arguments into NANs.</span></div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;  Packet4f zero_or_nan_if_inf = psub(_x, _x);</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;  x = padd(x, zero_or_nan_if_inf);</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;  <span class="comment">// Prevent sin/cos from generating values larger than 1.0 in magnitude</span></div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;  <span class="comment">// for very large arguments by setting x to 0.0.</span></div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;  Packet4i small_or_nan_mask = __builtin_msa_fcult_w(x, p4f_sincos_max_arg);</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;  x = pand(x, (Packet4f)small_or_nan_mask);</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160; </div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;  <span class="comment">// Scale x by 4/Pi to find x&#39;s octant.</span></div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;  Packet4f y = pmul(x, p4f_cephes_FOPI);</div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;  <span class="comment">// Get the octant. We&#39;ll reduce x by this number of octants or by one more than it.</span></div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;  Packet4i y_int = __builtin_msa_ftrunc_s_w(y);</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;  <span class="comment">// x&#39;s from even-numbered octants will translate to octant 0: [0, +Pi/4].</span></div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;  <span class="comment">// x&#39;s from odd-numbered octants will translate to octant -1: [-Pi/4, 0].</span></div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;  <span class="comment">// Adjustment for odd-numbered octants: octant = (octant + 1) &amp; (~1).</span></div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;  Packet4i y_int1 = __builtin_msa_addvi_w(y_int, 1);</div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;  Packet4i y_int2 = (Packet4i)__builtin_msa_bclri_w((Packet4ui)y_int1, 0); <span class="comment">// bclri = bit-clear</span></div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;  y = __builtin_msa_ffint_s_w(y_int2);</div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160; </div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;  <span class="comment">// Compute the sign to apply to the polynomial.</span></div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;  Packet4i sign_mask = sine ? pxor(__builtin_msa_slli_w(y_int1, 29), (Packet4i)_x)</div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;                            : __builtin_msa_slli_w(__builtin_msa_addvi_w(y_int, 3), 29);</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160; </div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;  <span class="comment">// Get the polynomial selection mask.</span></div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;  <span class="comment">// We&#39;ll calculate both (sin and cos) polynomials and then select from the two.</span></div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;  Packet4i poly_mask = __builtin_msa_ceqi_w(__builtin_msa_slli_w(y_int2, 30), 0);</div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160; </div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;  <span class="comment">// Reduce x by y octants to get: -Pi/4 &lt;= x &lt;= +Pi/4.</span></div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;  <span class="comment">// The magic pass: &quot;Extended precision modular arithmetic&quot;</span></div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;  <span class="comment">// x = ((x - y * DP1) - y * DP2) - y * DP3</span></div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;  Packet4f tmp1 = pmul(y, p4f_minus_cephes_DP1);</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;  Packet4f tmp2 = pmul(y, p4f_minus_cephes_DP2);</div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;  Packet4f tmp3 = pmul(y, p4f_minus_cephes_DP3);</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;  x = padd(x, tmp1);</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;  x = padd(x, tmp2);</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;  x = padd(x, tmp3);</div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160; </div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;  <span class="comment">// Evaluate the cos(x) polynomial.</span></div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;  y = p4f_coscof_p0;</div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;  Packet4f z = pmul(x, x);</div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;  y = pmadd(y, z, p4f_coscof_p1);</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;  y = pmadd(y, z, p4f_coscof_p2);</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;  y = pmul(y, z);</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;  y = pmul(y, z);</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;  y = __builtin_msa_fmsub_w(y, z, p4f_half);</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;  y = padd(y, p4f_1);</div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160; </div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;  <span class="comment">// Evaluate the sin(x) polynomial.</span></div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;  Packet4f y2 = p4f_sincof_p0;</div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;  y2 = pmadd(y2, z, p4f_sincof_p1);</div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;  y2 = pmadd(y2, z, p4f_sincof_p2);</div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;  y2 = pmul(y2, z);</div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;  y2 = pmadd(y2, x, x);</div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160; </div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;  <span class="comment">// Select the correct result from the two polynomials.</span></div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;  y = sine ? (Packet4f)__builtin_msa_bsel_v((v16u8)poly_mask, (v16u8)y, (v16u8)y2)</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;           : (Packet4f)__builtin_msa_bsel_v((v16u8)poly_mask, (v16u8)y2, (v16u8)y);</div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160; </div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;  <span class="comment">// Update the sign.</span></div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;  sign_mask = pxor(sign_mask, (Packet4i)y);</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;  y = (Packet4f)__builtin_msa_binsli_w((v4u32)y, (v4u32)sign_mask, 0); <span class="comment">// binsli = bit-insert-left</span></div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;  <span class="keywordflow">return</span> y;</div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;}</div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160; </div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;psin&lt;Packet4f&gt;(<span class="keyword">const</span> Packet4f&amp; x) {</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;  <span class="keywordflow">return</span> psincos_inner_msa_float&lt;<span class="comment">/* sine */</span> <span class="keyword">true</span>&gt;(x);</div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;}</div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160; </div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f</div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;pcos&lt;Packet4f&gt;(<span class="keyword">const</span> Packet4f&amp; x) {</div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;  <span class="keywordflow">return</span> psincos_inner_msa_float&lt;<span class="comment">/* sine */</span> <span class="keyword">false</span>&gt;(x);</div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;}</div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160; </div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2d</div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;pexp&lt;Packet2d&gt;(<span class="keyword">const</span> Packet2d&amp; _x) {</div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;  <span class="comment">// Limiting double-precision pexp&#39;s argument to [-1024, +1024] lets pexp</span></div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;  <span class="comment">// reach 0 and INFINITY naturally.</span></div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(exp_lo, -1024.0);</div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(exp_hi, +1024.0);</div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);</div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);</div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);</div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);</div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);</div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);</div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);</div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);</div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);</div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);</div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(half, 0.5);</div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(1, 1.0);</div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;  <span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(2, 2.0);</div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160; </div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;  Packet2d x = _x;</div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160; </div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;  <span class="comment">// Clamp x.</span></div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;  x = (Packet2d)__builtin_msa_bsel_v((v16u8)__builtin_msa_fclt_d(x, p2d_exp_lo), (v16u8)x,</div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;                                     (v16u8)p2d_exp_lo);</div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;  x = (Packet2d)__builtin_msa_bsel_v((v16u8)__builtin_msa_fclt_d(p2d_exp_hi, x), (v16u8)x,</div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;                                     (v16u8)p2d_exp_hi);</div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160; </div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;  <span class="comment">// Round to nearest integer by adding 0.5 (with x&#39;s sign) and truncating.</span></div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;  Packet2d x2_add = (Packet2d)__builtin_msa_binsli_d((v2u64)p2d_half, (v2u64)x, 0);</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;  Packet2d x2 = pmadd(x, p2d_cephes_LOG2EF, x2_add);</div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;  Packet2l x2_long = __builtin_msa_ftrunc_s_d(x2);</div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;  Packet2d x2_long_d = __builtin_msa_ffint_s_d(x2_long);</div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160; </div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;  x = __builtin_msa_fmsub_d(x, x2_long_d, p2d_cephes_exp_C1);</div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;  x = __builtin_msa_fmsub_d(x, x2_long_d, p2d_cephes_exp_C2);</div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160; </div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;  x2 = pmul(x, x);</div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160; </div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;  Packet2d px = p2d_cephes_exp_p0;</div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;  px = pmadd(px, x2, p2d_cephes_exp_p1);</div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;  px = pmadd(px, x2, p2d_cephes_exp_p2);</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;  px = pmul(px, x);</div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160; </div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;  Packet2d qx = p2d_cephes_exp_q0;</div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;  qx = pmadd(qx, x2, p2d_cephes_exp_q1);</div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;  qx = pmadd(qx, x2, p2d_cephes_exp_q2);</div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;  qx = pmadd(qx, x2, p2d_cephes_exp_q3);</div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160; </div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;  x = pdiv(px, psub(qx, px));</div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;  x = pmadd(p2d_2, x, p2d_1);</div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160; </div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;  <span class="comment">// x *= 2**exponent.</span></div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;  x = __builtin_msa_fexp2_d(x, x2_long);</div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160; </div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;  <span class="keywordflow">return</span> x;</div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;}</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160; </div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;}  <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160; </div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;}  <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160; </div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;<span class="preprocessor">#endif  </span><span class="comment">// EIGEN_MATH_FUNCTIONS_MSA_H</span></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition:</b> Core:139</div></div>
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